A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 309 people over the age of 55, 77 dream in black and white, and among 309 people under the age of 25, 18 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test H_0 : p_1 not equal to p_2 H_1 : p_1 = p_2 H_0 : p_1 = p_2 H_1 : p_1< p_2 H_0 : p_1 greater than or equal to p_2 H_1 : p_1 not equal to p_2 H_0 : p_1 = p_2 H_1 : p_1 not equal to p_2 Identify the test statistic. Identify the P-value. P-value = What is the conclusion based on the hypothesis test The P-value is the significance level of a = 0.05, so the null hypothesis. There is evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Test the claim by constructing an appropriate confidence interval. The 90% confidence interval is < (p_1 -p_2)< . What is the conclusion based on the confidence interval Because the confidence interval limits 0, it appears that the two proportions are Because the confidence interval limits include values, it appears that the proportion of people over 55 who dream in black and white is the proportion for those under 25. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.